The normal distribution function with μ=0 and standard deviation σ is given as follows a) b) d) f(x)= 1 σπ exp )) By using normal distribution function calculate fourteen equally spaced points in the interval x[μ-30,μ+30] for σ =2. Find the Newton interpolation polynomial that curve fits the data for each interval. Output the coefficients of the polynomial. Illustrate the individual points and Newton polynomial function in a) and b). respectively on a single plot. Fit the data obtained in (b) by using quadratic spline for the interval xe[u-30, +30] for σ = 2. Illustrate the individual points and quadratic spline function in a) and d), respectively on a single plot. f) Justify your result.